Problem Set 1

Assigned: Sept. 24
Due: Oct. 8

1. Write an algorithm for a bottom-up chart parser. You should use the
same form of edges as in the book's algorithm, but construct the edges
working up from the words of the sentence to the root of the tree.
You may assume that no rules have an empty right-hand side.

B) Give an example of an edge that will be constructed in a top-down
parse but not in a bottom-up parse.

C) Give an example of an edge that will be constructed in a bottom-up
parse but not in a top-down parse.

D) Give an example of an edge that will be constructed both in a top-down
parse and in a bottom-up parse, but is not part of either parse tree.

3) One of the parse tree in (2A) is very much more plausible than the other.
Describe a simple method for choosing the preferred tree.

4) (Open-ended)
Even if "catches" is correctly identified as a transitive verb, it
has a number of different meanings:

Jack catches a fish.
Jack catches a cold.
Jack catches the train.
Jack catches sight of Jill.
Jack caught the last ten minutes of Seinfeld.
Jack caught his foot on the rug

Discuss the use of selectional restrictions in finding the correct
interpretation of each of these sentences. For each of these, you should
propose a rule that will be satisfied by the correct interpretation.
Try to formulate your rule at a reasonably general level, and give one
or two other examples of sentences where the rule applies. If you do not
think that selectional restrictions are a suitable technique for the example,
explain why not and propose another method.

Note: Finding the "best" level of generality is by no means easy. For instance,
one can say

1) Jack catches the train to New York every morning.
2) Jack takes the bus to New York every morning.
3) Jack takes his car to New York every morning.

But you cannot say:

4) * Jack catches his car to New York every morning.

It would be difficult or impossible to propose a single rule that will include
(1), (2), and (3) but will exclude (4). So your rule for (1) must either
exclude (2), despite their apparent similarity, or must include (2) but
exclude (3), despite their apparent similarity.